Playing as France, my initial thoughts were to build a big empire with big cities and take advantage of the Commercial and Industrial traits for a Spaceship launch. Therefore my initial expansion was pretty wide; I was going for minimal overlap between adjacent cities. This might be a problem at Deity, because these cities need a lot of development and they are too far apart to support each other well early on, but I forged on.
I learned Pottery before I met the Arabs (my first two warriors went West and East!), and initially built 3 Warriors, a Granary, then a Settler. Settled to the North near the Wheat on Plains space and then successively on nearby bonus food sources; these cities built Granaries early on while Paris built a Warrior or 2 between Settlers. Expansion went pretty well.
I saw Green border to the West across the Water, so I left a Warrior down in that general area. After the Arabs came Portugal (trading for BW, CerBur and War Code between the two), and eventually the Aztecs crossed the water. That was the extent of my contacts during the AA.
After Pottery came Writing, which I researched first in my group, and traded for Wheel and Math. (Interesting they learned Math early.) Next was Philosophy; I was sweating as I saw Portugal learn Code-of-Laws and Map-Making, but in 1450 I learned Philosophy ... and that was it. Well, from other posts I was about 8 turns too late. In 1375 I contacted the Aztecs, who had Construction, so I suspected it was Monte who did Phil first. Phil gained me IW and Myst, and I limped towards Currency.
That took a while. Actually learned it uniquely in 750 BC, but Monte still held a monopoly on Construction! So no trade for that Tech, but I got all the others. Started on Construction, and finally one of the other AI on my civ learned Construction a few turns later, and I could make a trade; entered MidAges in 650 BC.
I eventually met the Romans when they founded on my continent, and Egypt sailed a Galley by also. Contact with the Incans and Byzantine didn't occur until Printing Press was learned by somebody. They were well behined everybody else, and Byzantine empire was small; they must have tussled with the Incas early on; neither was much of a player in the game.
Expansion went well, but there was a lot of space to claim. Arabs got to three 2nd tier city sites before me, and the Aztecs got two sites as well, so I didn't quite get all the locations I was aiming for.
Demands - quite a few which I paid off every time, usually 10-20 gold. I was in no shape for war.
The AI really started to pull past me in the early Middle Ages. I went for Engineering (learned that one from GOTM43!), and was eventually beaten to it in 150 BC; still, able to buy the remainder and Trade for Mono and Rep. Couldn't quite get Feudalism and Rep, but I really wanted to revolt so it was the best deal I could swing. That meant I had to learn Feud on my own with no trade options. Which I started on in 10 BC after a 7 turn anarchy (ouch!)
I would research a Tech for several turns, then buy the remaining research off one of the AI; Aztecs were huge in my game, and usually they lead with Arabs right behind, followed shortly by Portugal and Rome. Feud in 110 AD - no trades. I started crawling along the lower track, with the AI definitely ahead. Invention in 250 AD - no trades. Gunpowder in 310 AD - got two Luxuries to trade for! Starting to see some daylight. Chemistry in 380 AD - no trades. Only Aztecs have Metallurgy - start on it! Metallurgy in 430 AD - no trades, as the others make up the difference. Only Aztecs have MT - can I get it next! MT in 460 AD (big bucks to buy it here) - and I'm able to trade it for Education and Astronomy! Physics in 510 AD - I can get 3 Luxuries out of Physics (20 turns after the Gunpowder trade). Some of the AI have Magnetism, so go for ToG, bought in 540 AD - trade for Mag and Banking, and enter the Industrial Age! The key thing I was looking for was when a 2nd AI, usually the Arabs, got the Tech; this drops the price substantially and there are still two other AI (Rome and Portugal) to trade with.
I had huge debts at the beginning of the IA, time to recoup. Start building Banks, and set minimal research on Steam Power. And start building up to take the Arabs on; I had seen an early war between Arabs and Portugal that Portugal got the worst of, so I figured the Arabs were a little weaker and had already done a GA, and Portugal would be a willing ally. Also, I had no trades with them, and huge Gold payments to the Aztecs, so no deals to break and if the Aztecs decided to gang up on me, I'd be a lot richer. Disconnect Saltpeter, build some Horses, reconnect and upgrade. Hoping to get enough Cavalry before Riflemen show up, but didn't quite make it. Eventually got the war going, and brought Portugal, Aztecs and Rome in on it (in the end I decided it was worth the price.) After 20 turns I had taken about a 3rd of the Arab cities (Cav did OK against the Rifles they came up against), Aztecs another couple, Portugal had regained its losses plus a city or town, and even the Egyptians had chimed in and taken a city. Arabs were down to 3 cities, so I did not renew the alliances, and signed Peace. 2 turns later they were gone, so no chance for any more flips (a couple did happen, which were promptly recaptured). A successful war and set of alliances that saw me gain several Gems (a 3rd luxury) and an additional incense.
Now the issue is catching up, again. The AI learned Nationalism first, and then Medicine of all things. I decided to Gift Theodora into the IA to see if she got Steam Power - nope, Medicine. So I eventually buy Steam Power once two AI knew it, in 790 AD (about 3 turns into the big Arab war) and trade for Medicine. Next was Electricity, and I was surprised to see the AI beat me to it; I was able to trade for Industrialism. Next was Corporation, beaten to it again, and traded for Sanitation. Cities were building Factories, then Coal Plants and Hospitals. Now I set my sights on Steel, and I started to see Refining show up, and heard about somebody building the Theory of Evolution. Timing was going to be tight, but here's what happened between 1120 and 1130 AD:
and
Of course I have a Palace pre-build going. Steel, my first uniquely learned Tech of the game (ok, 2nd, after Currency), and it gets me Theory of Evolution, along with 2 free Techs, 3 required Techs from the AI, several optional Techs and tons of Gold the AI (mostly Aztecs and quite a bit of Roman gold) has been storing for me.

The rest was quite uneventful. AI beat me to Combustion so I bought the last turn, and researched Mass Prod and MotorTransp myself, trading for Flight. Gifted Theodora to Modern Era - she got Computers (hmm, 0 for 2), so I had to learn Fission myself and conclude a Diplo win (5-1 vs Monte; Egypt was also taken out) in 1325 AD. I was tired, and there was only 3 hours left to submit, so it seemed the prudent thing to do.
Another fun game; thanks Renata! I think Deity games just have to be played (since they come around infrequently), but next time, not two in a row, please!